The.or. Appl. G e n e t . 49 (1977) 111-115

W

9 by Springer-Verlag 1977

Effects of Linkage and Interaction in a Comparison of Theoretical Populations Derived by Diploidized Haploid and Single Seed Descent Methods T . J . Riggs and J . W . Snape Plant Breeding Institute, Trumpington, Cambridge (England) S u m m a r y . C o m p a r i s o n s w e r e m a d e b e t w e e n the g e n e t i c m e a n s and v a r i a n c e s of a q u a n t i t a t i v e t r a i t d e t e r m i n e d by 8 loci i n s i m u l a t e d p o p u l a t i o n s of l i n e s d e r i v e d by d i p l o i d i z i n g h a p l o i d s (DH) on the one hand and by s i n g l e s e e d d e s c e n t (SSD) on the o t h e r . In the a b s e n c e of l i n k a g e no d i f f e r e n c e s b e t w e e n the p o p u l a t i o n s w e r e o b s e r v e d , but when l i n k a g e was p r e s e n t , r e c o m b i n a t i o n was m o r e f r e q u e n t i n the SSD p o p u l a t i o n s as i n d i c a t e d by the r e l a t i v e d i f f e r e n c e s in v a r i a n c e b e t w e e n t h e s e and the DH p o p u l a t i o n s . In addition, d i f f e r e n c e s in m e a n s b e t w e e n the p o p u l a t i o n s d e r i v e d by the two m e t h o d s w e r e o b s e r v e d when n o n - a l l e l i c i n t e r a c t i o n was p r e s e n t . The d i r e c t i o n and m a g n i t u d e of the d i f f e r e n c e s in both m e a n s and v a r i a n c e s d e p e n d e d upon the l i n k a g e p h a s e , the r e c o m b i n a t i o n f r e q u e n c y a n d the p r e s e n c e o r a b s e n c e of i n t e r a c t i o n . The c o n c l u s i o n was d r a w n that the SSD m e t h o d was to be p r e f e r r e d f r o m t h e o r e t i c a l c o n s i d e r a t i o n s although i n p r a c t i c e the c h o i c e of m e t h o d will a l s o depend upon p r a c t i c a l and t e c h n i c a l f a c t o r s . Introduction The d e v e l o p m e n t of m e t h o d s for h a p l o i d p r o d u c t i o n i n h i g h e r p l a n t s has i m p l i c a t i o n s not only for g e n e t i c a l r e s e a r c h but also for the r a p i d d e v e l o p m e n t of t r u e b r e e d i n g l i n e s a m o n g s t which s e l e c t i o n c a n t h e n be p r a c t i s e d i n a p r a c t i c a l b r e e d i n g p r o g r a m m e . In b a r l e y , Horde~w v u l g a t e L . , high f r e q u e n c i e s of haploids have b e e n o b s e r v e d following i n t e r - s p e c i f i c h y b r i d i z a t i o n s b e t w e e n H. vulgate (2n = 2x = 14) and H. bulbosum (2n = 2x = 14) ( s e e K a s h a 1974 for r e v i e w ) , and t e c h n i q u e s for the p r o d u c t i o n of b a r l e y h a p l o i d s and t h e i r s u b s e q u e n t c h r o m o s o m e doubling have s i n c e i m p r o v e d s u f f i c i e n t l y for the u t i l i s a t i o n of doubled h a p l o i d s i n b r e e d i n g p r o g r a m m e s ( K a s h a and R e i n b e r g s 1972; P a r k et al. 1976). R e c e n t l y B a r c l a y (1975) showed that h a p l o i d s c o u l d also be p r o d u c e d i n wheat by c h r o m o s o m e e l i m i n a t i o n a f t e r the i n t e r - g e n e r i c c r o s s b e t w e e n Trit~eum aest~vum ( 2 n = 6x = 42) and H. bulbosum ( 2 n = 2x = 14 a n d 2 n = 4x = 2 8 ) . A l t e r n a t i v e l y , r a p i d p r o d u c t i o n of n e a r - h o m o z y g o u s

m a r 1975; B o e r m a and C o o p e r 1975; C a s a l i and Tigc h e l a a r 1975). In m o s t c a s e s SSD was c o n s i d e r e d to have c o n s i d e r a b l e m e r i t b e c a u s e of the g e n e r a l l y s h o r t t i m e r e q u i r e d to develop h o m o z y g o u s l i n e s , the l a r g e g e n e t i c v a r i a n c e o b s e r v e d a m o n g s t t h e s e l i n e s , and the g e n e t i c g a i n s o b t a i n e d a f t e r s e l e c t i o n . Snape and Riggs (1975) d e s c r i b e d the g e n e t i c a l c o n s e q u e n c e s of SSD and c o n c l u d e d that whilst g e n e t i c a d v a n c e m a y not be as g r e a t in s o m e g e n e t i c a l s i t u a t i o n s as might be e x p e c t e d a f t e r efficient p e d i g r e e s e l e c t i o n , the m e t h o d n e v e r t h e l e s s had c o n s i d e r a b l e a d v a n t a g e s . S i m i l a r c o n c l u s i o n s w e r e d r a w n by B l i s s and G a t e s (1968) f r o m a c o m p u t e r s i m u l a t i o n s t u d y c o m p a r i n g SSD with m a s s s e l e c t i o n . J i n k s and Pooni (1975) showed that the p e r f o r m a n c e of i n b r e d l i n e s d e r i v e d by s i n g l e s e e d d e s c e n t c o u l d be p r e d i c t e d f r o m the g e n e t i c p a r a m e t e r s e s t i m a t e d f r o m the p a r e n t s , F 1 , F 2 and b a c k c r o s s g e n e r ations. Using c o m p u t e r s i m u l a t i o n , W a l s h (1974) c o m p a r e d l i n e s g e n e r a t e d by the DH and p e d i g r e e s e l e c -

l i n e s c a n be a c h i e v e d by the s i n g l e s e e d d e s c e n t (SSD)

t i o n m e t h o d s and c o n c l u d e d that the DH m e t h o d would

p r o c e d u r e ( G o u l d e n 1939; B r i m 1966; K a u f m a n n 1961,

be s u p e r i o r only when s e l e c t i n g for a q u a n t i t a t i v e t r a i t

1971 ; Riggs and H a y t e r 1976). In t h i s m e t h o d s e g r e g a -

with low h e r i t a b i l i t y .

ting g e n e r a t i o n s a r e r a p i d l y a d v a n c e d in the g l a s s h o u s e

P a r k et al. (1976) r e p o r t e d c o m p a r a t i v e m e a s u r e -

with no s e l e c t i o n , each l i n e being c o n t i n u e d by a s i n g l e

m e n t s m a d e i n p o p u l a t i o n s of h o m o z y g o u s b a r l e y l i n e s

s e e d i n each g e n e r a t i o n .

p r o d u c e d by SSD and by DH m e t h o d s . They o b s e r v e d

C o m p a r i s o n s i n plant b r e e d i n g p r a c t i c e of SSD with

s i g n i f i c a n t d i f f e r e n c e s b e t w e e n SSD and DH p o p u l a -

e a r l y g e n e r a t i o n s e l e c t i o n and t e s t i n g have b e e n m a d e

t i o n m e a n s for g r a i n y i e l d , plant height and h e a d i n g

by s e v e r a l w o r k e r s in a r a n g e of c r o p s (Knott and K u -

date. Since p r e v i o u s work had i n d i c a t e d the r a n d o m -

ll2

T . J . R i g g s and J . W . Snape: E f f e c t s of Linkage and I n t e r a c t i o n p u t e r s i m u l a t i o n s t u d i e s a i m e d at c o m p a r i n g the v a r -

4.0 ~,, 3.5

Coupling \

3.0 ~

~ ' ~

-,,, ~'",

. . . .

9

~,~-..,. CoupUng

te seeddescent '" ~ ' I . Di oidized hoploids- -

~ . "-~

2.5

s

"-~,=,2.0 1.5 1.0 0.5 //

9

Z

~ ,~, .,,/,-

/-

/4 Reputsion

/

!

i a n c e s in p o p u l a t i o n s d e r i v e d r e s p e c t i v e l y by DH o r SSD when l i n k a g e is p r e s e n t . The e f f e c t s of c o m p l e m e n t a r y n o n - a l l e l i c i n t e r a c t i o n s on t h e p o p u l a t i o n

o~

m e a n s and v a r i a n c e s a r e a l s o d e s c r i b e d .

/

/

Methods

/Y /

! / / Repulsion

u

O0 0.1 0.2 0.3 0.4. 0.5 0 0.1 0.2 0.3 0.4 0.5 a. Recombinotionfrequencyp b Recombin(]lionfrequencyp F i g . 1. The 2 - l o c u s m o d e l : e x p e c t e d v a r i a n c e s with c h a n g e in r e c o m b i n a t i o n f r e q u e n c y ( p ) , and o b s e r v e d values for simulated populations. a) No i n t e r a c t i o n , b) C o m p l e m e n t a r y i n t e r a c t i o n o single seed descent ...... 9 diploidized haploids

n e s s of DH p o p u l a t i o n s , t h e y i n f e r r e d that s o m e s e l e c t i o n was i n h e r e n t in the SSD m e t h o d as p r a c t i c e d . In t e s t i n g the a s s u m p t i o n that h a p l o i d p r o d u c t i o n r e s u l t s in a r a n d o m s a m p l e of g a m e t e s p r o d u c e d f r o m a heterozygous genotype, workers have looked for s i m i l a r r a n g e s and v a r i a n c e s in DH p o p u l a t i o n s and p o p u l a t i o n s d e r i v e d by s e l l i n g . H o w e v e r , when l i n k a g e i s p r e s e n t , t h e c o m p o s i t i o n s of t h e two p o p u l a t i o n s would d i f f e r e v e n a s s u m i n g no d i f f e r e n t i a l s u r v i v a l of g a m e t e s . Snape (1976) h a s shown t h e o r e t i c a l l y that when l i n k a g e i s p r e s e n t t h e g e n e t i c a l c o n s e q u e n c e s of t h e DH and SSD m e t h o d s will be d i f f f e r -

The s i m u l a t i o n p r o c e d u r e w as c a r r i e d out f or 8 l o c i a s s o r t i n g i n d e p e n d e n t l y in t h e a b s e n c e of l i n k a g e o r , when l i n k a g e w as p r e s e n t , d i s t r i b u t e d as 2 l o c i in e a c h of f o u r l i n k a g e g r o u p s , as 4 l o c i in e a c h of two l i n k a g e g r o u p s o r as 8 l o c i in a s i n g l e l i n k a g e g r o u p . All l o c i w e r e of equal e f f e c t . R e c o m b i n a t i o n f r e q u e n c i e s (p) b e t w e e n a d j a c e n t l o c i in t h e s a m e l i n k a g e g r o u p w e r e s e t at 0 . 4 5 , 0 . 2 5 o r 0 . 0 5 and i n t e r f e r e n c e w as a s s u m e d a b s e n t . The F~ b e t w e e n t h e p a r e n t s w as h e t e r o z y g o u s at all l o c i , which w e r e a r r a n g e d in c o u p l i n g (+_1111+11), r e p u l s i o n (1~131~1~) o r in m i x e d c o u p l i n g and r e p u l s i g n p h a s e s (+1++~+~+_). Two s i t u a t i o n s of g e n e a c t i o n w e r e a s s u m e d : (i) a d d i t i v e e f f e c t s with c o m p l e t e d o m i n a n c e f o r i n creasing alleles ; ( i i ) a d d i t i v e e f f e c t s with c o m p l e t e d o m i n a n c e f o r i n c r e a s i n g a l l e l e s and c o m p l e m e n t a r y g e n e i n t e r a c t i o n s . Genotype values w e r e calculated using m = 10.0, d = + 0 . 5 , h = + 0 . 5 and f o r c o m p l e m e n t a r y g e n e i n teraction between homozygous loci, i = + 0.5. G a m e t o g e n e s i s in t h e F~ w as s i m u l a t e d u s i n g the m e t h o d of b i n a r y m a s k s as d e s c r i b e d by F r a s e r and B u r n e l l ( 1970). In g e n e r a t i n g t h e d i p l o i d i z e d h a p l o i d s e a c h g a m e t e was s i m p l y d u p l i c a t e d to f o r m a h o m o z y g o u s d i p l o i d i n d i v i d u a l . A p o p u l a t i o n of 500 s u c h i n d i v i d u a l s was g e n e r a t e d and the m e a n and v a r i a n c e c o m p u t e d . F o r t h e s i m u l a t i o n of s i n g l e s e e d d e s c e n t an F~ of 500 i n d i v u d u a l s was f i r s t g e n e r a t e d . Single p r o g e n y d e s c e n t was t h e n s i m u l a t e d f o r t h r e e g e n e r a t i o n s . In the Fs, f a m i l i e s of 10 p r o g e n y w e r e g e n e r a t e d f r o m e a c h F5 i n d i v i d u a l , and t h e f a m i l y m e a n s a n d v a r i a n c e s c o m p u t e d . The o v e r a l l p o p u l a t i o n m e a n and t he b e t w e e n - f a m i l y v a r i a n c e was t h e n d e t e r m i n e d . The c o m p u t e r p r o g r a m m e f o r t h e s e o p e r a t i o n s was w r i t t e n in F O R T R A N IV and r u n on t h e IBM 370/165 c o m p u t e r at t h e C a m b r i d g e U n i v e r s i t y C o m p u t e r Laboratory.

ent: f o r a 2 - l o c u s m o d e l t h e f r e q u e n c y of r e c o m b i nants was g r e a t e r in p o p u l a t i o n s p r o d u c e d by SSD. T e c h n i c a l and p r a c t i c a l d i f f i c u l t i e s m a y be e x -

R e s u l t s and D i s c u s s i o n

p e r i e n c e d in t h e u s e of e i t h e r m e t h o d a n d t h e b r e e d e r ' s

Mean data a r e p r e s e n t e d f r o m two r u n s of t he p r o -

c h o i c e m a y be d e t e r m i n e d by th e a v a i l a b i l i t y of f a c i l -

g r a m m e f o r e a c h c o m b i n a t i o n of g e n e t i c a l s i t u a t i o n

i t i e s and e x p e r t i s e and th e r e l a t i v e t i m e - s c a l e s of the

and l i n k a g e a r r a n g e m e n t . R e s i d u a l h e t e r o z y g o s i t y in

two m e t h o d s . He m a y a l s o h a v e no p r i o r k n o w l e d g e

the SSD l i n e s was g e n e r a l l y v e r y low and c o n s e q u e n t l y

as to t h e d e g r e e of l i n k a g e b e t w e e n t h e g e n e s u n d e r

within-family v a r i a n c e s w e r e absent o r negligible,

s e l e c t i o n . N e v e r t h e l e s s an u n d e r s t a n d i n g of t h e d i f -

and would not m a t e r i a l l y affect t h e r e s u l t s .

f e r i n g g e n e t i c a l c o n s e q u e n c e s of t h e two m e t h o d s when

The f o u r l i n k a g e g r o u p s i t u a t i o n s s i m u l a t e d h e r e

l i n k a g e is p r e s e n t m a y be i m p o r t a n t in c h o i c e of m e t h -

c a n be c o n s i d e r e d to c o n s t i t u t e f o u r r e p l i c a t i o n s of t he

od o r i n t e r p r e t a t i o n of r e s u l t s .

2 - l o c u s m o d e l of Snape ( 1 9 7 6 ) . Thus t h e o b s e r v e d

In t h i s p a p e r we e x t e n d th e findings of Snape (1976)

c h a n g e in v a r i a n c e with c h a n g e in p c a n be c o m p a r e d

to a m u l t i - l o c u s m o d e l and d i s c u s s the r e s u l t s of c o m -

with the t h e o r e t i c a l e x p e c t a t i o n s . F i g u r e 1 s h o w s t he

T . J . R i g g s and J . W . Snape: E f f e c t s of Linkage and I n t e r a c t i o n

Tab l e 1. V a r i a n c e s f o r p o p u l a t i o n s d e r i v e d b y S S D is p r e s e n t

113

o r DH when l i n k a g e , but n o t i n t e r a c t i o n ,

Initial l i n k a g e p h a s e Coupling

Repulsion

Mixed coupling/repulsion SSD

DH

p

SSD

DH

SSD

0.50

1.999

2.141

.

2 l i n k a g e g r o u p s / 0.45 0.25 of41oci / 0.05

2.017 3.482 6.184

2.171 4.078 * 7 . 6 0 8 **

1.951 1.132 0.341

1.688 * 0 .7 4 2 *** 0.149"**

1.972 2.288 3.432

2 .0 8 1 2.471 3 .6 8 5

0.45 0.25 0.05

2.114 3.819 10.413

2.502 * 5.157 *** 12.575 *

1.862 1.166 0.298

1.707 0.816 * * * 0 . 1 2 3 ***

2.074 2.020 2.920

2 .0 0 1 2.184 2 .5 0 1 *

No l i n k a g e

1 linkage group of 8 1 o c i *, **, ***: F -

r a t i o s i g n i f i c a n t at P < 0 . 0 5 ,

DH .

.

.

0 . 0 1 and 0 . 0 0 1 ~ r e s p e c t i v e l y , N x , N ~ = 499

Table 2. V a r i a n c e s f o r p o p u l a t i o n s d e r i v e d by SSD o r DH when l i n k a g e and c o m p l e m e n t a r y interaction are present Initial l i n k a g e p h a s e Coupling

Repulsion

Mixed coupling/repulsion

DH

SSD

DH

p

SSD

DH

SSD

No l i n k a g e

0.50

3.107

2.945

-

2 linkage groups of 4 l o c i

0.45 0.25 0.05

3.138 4.237 6.643

3.700 * 5.063 * 7.561

2 .8 0 1 2.204 0.646

2.753 1.487 *** 0 .2 6 6 ***

3.119 3.228 3.712

2 .7 8 2 3 .2 7 5 3.544

I 0.45 0.25 ~ 0.05

3.109 4.640 10.955

3.402 5 .4 9 4 * 12.590

2.779 2.064 0.683

2 .7 3 6 1.608 ** 0 .2 1 2 ***

3 .0 5 3 3.048 3.406

3.001 2.779 3 .4 9 3

I linkage group of81oci

o b s e r v e d v a r i a n c e s , t o g e t h e r with c u r v e s s h o w i n g t h e

b i n a t i o n h as a p r o p o r t i o n a t e l y g r e a t e r e f f e c t on t he

t h e o r e t i c a l t r e n d s , when i n i t i a l l i n k a g e was in e i t h e r

v a r i a n c e when i n i t i a l l i n k a g e was in c o u p l i n g t h a n

c o u p l i n g o r r e p u l s i o n and i n t e r a c t i o n w a s e i t h e r a b -

when in r e p u l s i o n . C l e a r l y t h e 2 - l o c u s m o d e l p r o -

s e n t ( F i g . l a ) o r p r e s e n t ( F i g . l b ) . The a g r e e m e n t

vides a symmetrical situation where recombination

sh o wn in both f i g u r e s w a s s a t i s f a c t o r y . Considering the other linkage a r r a n g e m e n t s , Table 1 s h o w s the o b s e r v e d v a r i a n c e s when no i n t e r a c t i o n was p r e s e n t . A s e x p e c t e d , l o w r e c o m b i n a t i o n f r e q u e n c i e s w e r e a s s o c i a t e d with high p o p u l a t i o n v a r i a n c e s when t h e i n i t i a l l i n k a g e p h a s e was in c o u p l i n g and l o w v a r i a n c e s when l i n k a g e w a s in r e p u l s i o n . A h i g h e r p r o p o r t i o n of r e c o m b i n a n t s in t h e SSD p o p u l a t i o n was i n d i c a t e d by c o n s i s t e n t l y l o w e r v a r i a n c e r e l a t i v e to t h e DH p o p u l a t i o n , when i n i t i a l l i n k a g e was in c o u p l i n g , and h i g h e r v a r i a n c e when l i n k a g e w a s in r e p u l s i o n .

r e s u l t s in a shift f r o m o n e l i n k a g e p h a s e to the o t h e r . In a m u l t i - l o c u s m o d e l with l o c i of eq u al o r s i m i l a r e f f e c t , i n f r e q u e n t c r o s s - o v e r e v e n t s a r e s e e n to h a v e r e l a t i v e l y l e s s e f f e c t on p o p u l a t i o n v a r i a n c e when l i n k a g e is i n i t i a l l y in r e p u l s i o n t h a n when it is in c o u p l i n g . This is a s c a l i n g e f f e c t due to t h e high v a r i a n c e b e t w e e n h o m o z y g o t e s in c o u p l i n g , and c a n be s e e n a l s o in t h e p o p u l a t i o n s h a v i n g m i x e d c o u p l i n g and r e pulsion phase linkage groups, where there was a pos i t i v e t r e n d in t h e v a r i a n c e as p d e c r e a s e d . In t h e p r e s e n c e of c o m p l e m e n t a r y i n t e r a c t i o n (Table 2 ), v a r i a n c e s w e r e g e n e r a l l y h i g h e r as e x p e c t e d (Snape and R i g g s 1975). F o r t h e 2 - l o c u s m o d e l t he

In t h e c a s e s of one o r two l i n k a g e g r o u p s of 8 o r

c h a n g e in v a r i a n c e with p i s e x p e c t e d to be l e s s when

4 l o c i r e s p e c t i v e l y , d i f f e r e n c e s f r o m th e 2 - l o c u s

l i n k a g e is i n i t i a l l y in c o u p l i n g t h a n when in r e p u l s i o n

m o d e l a r e c l e a r l y a p p a r e n t in that r e s t r i c t e d r e c o m -

( F i g . l b ) . H o w e v e r , f o r t h e m u l t i l o c u s s i t u a t i o n s the

114

T . J . R i g g s and J . W . Snape: E f f e c t s of Linkage and I n t e r a c t i o n Table 3. M e a n s f o r p o p u l a t i o n s d e r i v e d by SSD o r DH when l i n k a g e and c o m p l e m e n t a r y i n t e r a c t i o n is p r e s e n t Initial l i n k a g e p h a s e Coupling p

SSD

No l i n k a g e

0.50

10.07

9.98

2 linkage groups of 4 l o c i

0.45 0.25 0.05

10.10 10.82 11.67

10.26 11.01 1 1 .7 0

9.12 9.54 11.78

9.22 9.87 11.80

I linkage

group

of81oci

I 0.45 0.25 I 0.05

DH

~

Repulsion

Mixed coupling/repulsion

SSD

DH

SSD

DH

-

-

9.91 9.38 8.38

9.75 8.95 ~ 8.13 ~

10.03 10.04 10.05

10.01 10.02 10.00

9.88 9.28 8.41

9.81 9.05 8.11

9.95 9.05 9.95

10.03 9.90 9.76

~ ~

~*~*

*, **, ***: s i g n i f i c a n c e at P < 0 . 0 5 , 0 . 0 1 , 0 .0 0 1 ~ r e s p e c t i v e l y f o r d i f f e r e n c e s b e t w e e n SSD and DH p o p u l a t i o n m e a n s s . e .

difference=

V VSSD0--dVDH

r e s p o n s e to c h a n g e in p f o r t h e c o u p l i n g a r r a n g e m e n t s

t h o s e of t h e SSD p o p u l a t i o n s with the g r e a t e s t d i f f e r e n c e

w as a g a i n v e r y m a r k e d . This f u r t h e r i l l u s t r a t e s the

at the i n t e r m e d i a t e v a l u e of p. This a g r e e s with t he

p r o p o r t i o n a t e l y g r e a t e r e f f e c t of r e c o m b i n a t i o n when

t h e o r y f o r t h e 2 - l o c u s m o d e l (Snape 1976).

m o r e than 2 l o c i a r e i n v o l v e d in c o u p l i n g l i n k a g e . F r o m T a b l e s 1 and 2 it c a n be s e e n that the d i f f e r e n c e

This was a l s o t h e c a s e f o r r e p u l s i o n l i n k a g e : the m e a n s w e r e g e n e r a l l y l o w e r than t h o s e when l i n k a g e

in v a r i a n c e b e t w e e n SSD and DH p o p u l a t i o n s , though not

was in c o u p l i n g , and in t h i s c a s e t h e m e a n s of t he SSD

always statistically significant, indicated a consistently

p o p u l a t i o n s e x c e e d e d t h o s e of t h e c o r r e s p o n d i n g DH

h i g h e r f r e q u e n c y of r e c o m b i n a t i o n i n t h e SSD p o p u l a t i o n s

p o p u l a t i o n s . All the m e a n s d e c r e a s e d with d e c r e a s e

when l i n k a g e was e i t h e r in c o u p l i n g o r r e p u l s i o n . This

in p. A g a i n t h e d i f f e r e n c e b e t w e e n t h e two p o p u l a t i o n s

was p a r t i c u l a r l y t h e c a s e , h o w e v e r , f o r r e p u l s i o n l i n -

was l a r g e at t h e i n t e r m e d i a t e r e c o m b i n a t i o n f r e q u e n c y

k a g e s in these

simulations,

and was

lowest

recombination

makes

it difficult to discern

linkages

frequency

in coupling

Where

differences

equal numbers

and repulsion

difference

could be observed

of the SSD

and DH

populations,

with coupling

with repulsion

of loci were

phase

at the

of 0.05 ~. Interaction

but inflates the differences

linkages.

maintained

linkage,

between

involved

no consistent

the variances

nor would

this be ex-

pected. In t h e a b s e n c e of i n t e r a c t i o n , no d i f f e r e n c e was

(p = 0 . 2 5 ) . W h e n equal n u m b e r s of l o c i w e r e i n v o l v e d in c o u p ling and r e p u l s i o n p h a s e l i n k a g e s , p o p u l a t i o n m e a n s w e r e i n t e r m e d i a t e and, with one e x c e p t i o n , did not d i f f e r m a r k e d l y b e t w e e n p o p u l a t i o n s d e r i v e d by the different methods. P r o d u c t i o n of h a p l o i d s f r o m an F~ h y b r i d l i m i t s t h e o p p o r t u n i t y f o r r e c o m b i n a t i o n b e t w e e n l o c i to a s i n g l e m e i o s i s . In the a b s e n c e of l i n k a g e an u n b i a s e d s a m p l e f r o m all p o s s i b l e g e n o t y p e s s h o u l d be o b t a i n e d

e x p e c t e d b e t w e e n the m e a n s of the SSD and DH p o p u -

but when l i n k a g e i s p r e s e n t , the f r e q u e n c y of r e c o m -

l a t i o n s , which, a p a r t f r o m s m a l l f l u c t u a t i o n s due to

binant g e n o t y p e s in a p o p u l a t i o n of d i p l o i d i z e d h a p l o i d s

s a m p l i n g , took t h e m i d - p a r e n t a l v a l u e f o r all r u n s .

will be r e l a t i v e l y l o w e r and t h e d e g r e e of l i n k a g e d i s -

When h o m o z y g o t e • h o m o z y g o t e (i) t y p e i n t e r a c t i o n s

e q u i l i b r i u m g r e a t e r than in an equal s i z e d p o p u l a t i o n

w e r e p r e s e n t , h o w e v e r , d i f f e r e n c e s in the p o p u l a t i o n

of l i n e s d e r i v e d b y s i n g l e s e e d d e s c e n t ( T a b l e s 1 a n d 2 ) .

m e a n s w e r e a p p a r e n t a s shown in Table 3. The d i r e c t i o n and m a g n i t u d e of t h e d i f f e r e n c e was sho wn by Snape (1976) f o r 2 l o c i to depend upon t h e

D i f f e r e n c e s d e t e c t e d in p r a c t i c e b e t w e e n DH and SSD p o p u l a t i o n s ( e . g .

P a r k et al. 1976) c o u l d be due

to l i n k a g e a n d / o r u n c o n s c i o u s s e l e c t i o n in t h e d e v e l -

i n i t i a l l i n k a g e p h a s e and t h e r e c o m b i n a t i o n f r e q u e n c y

o p m e n t of l i n e s by e i t h e r m e t h o d . Linkage with no i n -

r e s p e c t i v e l y . With c o u p l i n g l i n k a g e t h e m e a n s of both

t e r a c t i o n would l e a d to d i f f e r e n c e s in t h e v a r i a n c e s

p o p u l a t i o n s i n c r e a s e d as p d e c r e a s e d . The m e a n s of

only, w h i l s t s e l e c t i o n , o r l i n k a g e with i n t e r a c t i o n ,

the DH p o p u l a t i o n s w e r e a l w a y s h i g h e r o r equal to

would r e s u l t in d i f f e r e n c e s in v a r i a n c e s and m e a n s .

T . J . Riggs and J . W . Snape: E f f e c t s of Linkage and I n t e r a c t i o n

The h i g h e r p r o p o r t i o n of r e c o m b i n a n t g e n o t y p e s in p o p u l a t i o n s d e r i v e d by SSD when l i n k a g e is p r e s e n t , c o u l d be i m p o r t a n t w h e t h e r the s e v e r a l loci i n v o l v e d c o n t r o l the e x p r e s s i o n of only one c h a r a c t e r , as a s s u m e d h e r e , o r of two o r m o r e c h a r a c t e r s . Indeed, the e n h a n c e d o p p o r t u n i t y p r o v i d e d by SSD for the b r e a k i n g of a s s o c i a t i o n s b e t w e e n c h a r a c t e r s might be the m o r e i m p o r t a n t a d v a n t a g e . F r o m the b r e e d e r ' s point of view the m a i n i n t e r e s t will g e n e r a l l y be i n o b t a i n i n g the m a x i m u m v a r i a t i o n from a cross between parents usually complementing each o t h e r for s t r e n g t h s and w e a k n e s s e s and t h e r e f o r e l i k e l y to p r o d u c e an F 1 with loci m a i n l y i n r e p u l s i o n . If he w i s h e s to a c c e l e r a t e the p r o d u c t i o n of h o m o z y gous l i n e s f r o m s u c h a c r o s s , t h e o r e t i c a l c o n s i d e r a t i o n s s u g g e s t that the b r e e d e r should u s e SSD r a t h e r t h a n the DH m e t h o d , s i n c e l i n k a g e m a y be p r e s e n t . In addition, the DH m e t h o d m a y r e q u i r e c o n s i d e r a b l e e x p e r t i s e , and it m a y be difficult i n s o m e c i r c u m s t a n c e s to p r o d u c e and d i p l o i d i z e h a p l o i d s i n s u f f i c i e n t n u m b e r s to a d e q u a t e l y exploit the h y b r i d . This c o n s i d e r a t i o n a p a r t , the DH m e t h o d might be m o r e s u i t able for s p e c i e s having a r e l a t i v e l y l a r g e n u m b e r of c h r o m o s o m e s w h e r e new v a r i a t i o n would be r e l e a s e d m a i n l y as a r e s u l t of r e a s s o r t m e n t of c h r o m o s o m e s , a n d the i m p o r t a n c e of l i n k a g e would be r e l a t i v e l y l e s s than in s p e c i e s with f e w e r c h r o m o s o m e s . Although the r a t e of f a i l u r e in d i p l o i d i z e d h a p l o i d p r o d u c t i o n i n b a r l e y m a y be f a i r l y high, t h e r e is a p p a r e n t l y no e v i d e n c e that the l o s s e s a r e genotype s p e c i f i c ( K a s h a and R e i n b e r g s 1972; K a s h a 1974). L o s s e s d u r i n g SSD m a y also be high and t h e r e i s s o m e e v i dence for b a r l e y that t h e s e l o s s e s m a y not be r a n d o m l y d i s t r i b u t e d ( R i g g s and H a y t e r 1976). The s e r i o u s n e s s of t h i s p r o b l e m will depend upon the c r o p c o n c e r n e d and the a g r o n o m i c m e t h o d s u s e d .

B o e r m a , H . R . ; C o o p e r , R . L . : C o m p a r i s o n of t h r e e s e l e c t i o n p r o c e d u r e s for y i e l d i n s o y b e a n s . C r o p Sol. 15, 225-229 (1975) B r i m , C . A . : A m o d i f i e d p e d i g r e e m e t h o d of s e l e c t i o n i n s o y b e a n s . C r o p . Sci. 6, 220 (1966) Casali, V.W.D.; Tigchelaar, E.C. : Breeding prog r e s s i n t o m a t o with p e d i g r e e s e l e c t i o n and s i n g l e s e e d d e s c e n t . J . A m e r . Soc. H o r t . Sci. 1 0 0 ( 4 ) , 362-364 (1975) F r a s e r , A. ; B u r n e l l , D. : C o m p u t e r m o d e l s i n g e n e t i c s . London: M c G r a w - H i l l 1970 Goulden, C . H . : P r o b l e m s i n plant s e l e c t i o n . In: P r o c e e d i n g s of the Seventh I n t e r n a t i o n a l G e n e t i c s C o n g r e s s , C a m b r i d g e U n i v e r s i t y P r e s s , 132-133 (1939) J i n k s , J . L . ; Pooni, H.S. : P r e d i c t i n g the p r o p e r t i e s of r e c o m b i n a n t i n b r e d l i n e s d e r i v e d by s i n g l e s e e d d e s c e n t . H e r e d i t y 36, 253-266 (1976) K a s h a , K . J . : Haploids f r o m s o m a t i c c e l l s . In: Hapl o i d s i n H i g h e r P l a n t s , A d v a n c e s and P o t e n t i a l . ( E d i t o r K a s h a , K . J . P r o c e e d i n g s of the F i r s t I n t e r n a t i o n a l S y m p o s i u m on Haploids, U n i v e r s i t y of Guelph, C a n a d a , 67-87 (1974) K a s h a , K . J . ; R e i n b e r g s , E. : The h a p l o i d t e c h n i q u e i n b a r l e y b r e e d i n g . MBA Technical Q u a r t e r l y 9 ( 3 ) , 128-130 (1972) K a u f m a n n , M.L. : A p r o p o s e d m e t h o d of oat b r e e d i n g for C e n t r a l A l b e r t a . C e r e a l News 6, 15-18 (1961) K a u f m a n n , M. L. : The r a n d o m m e t h o d oToat b r e e d i n g for p r o d u c t i v i t y . Can. J . P l a n t Sci. 51, 13-16 (1971) Knott, D . R . ; K u m a r , J . : A c o m p a r i s o n of e a r l y g e n e r a t i o n y i e l d t e s t i n g and a s i n g l e s e e d d e s c e n t p r o c e d u r e i n wheat b r e e d i n g . C r o p Sci. 15, 295299 (1975) Park, S.J. ; Walsh, E.J. ; Reinbergs, E. ; Song, L.S.P. ; Kasha, K.J. : Field performance of doubled haploid barley lines in comparison with lines developed by the pedigree and single seed descent methods. CanJ. Plant Sci. 56, 467-474 (1976) Riggs, T . J . ; Hayter, A.M. : Practical aspects of the single seed descent method in barley breeding. In: Proceedings of the Third International Barley Genetics Symposium, Munich, 708-717 ( 1976 ) Snape, J.W. : A theoretical comparison of diploidized haploid and single seed descent populations. Heredity 36(2), 275-277 (1976) Snape, J . W . ; R i g g s , T . J . : G e n e t i c a l c o n s e q u e n c e s of s i n g l e s e e d d e s c e n t i n the b r e e d i n g of s e l f - p o l l i n a ting c r o p s . H e r e d i t y 3_~5(2), 211-219 ( 1975 ) Walsh, E . J . : E f f i c i e n c y of the h a p l o i d m e t h o d i n b r e e ding of a u t o g a m o u s diploid s p e c i e s : a c o m p u t e r s i m u l a t i o n study. In: Haploids i n H i g h e r P l a n t s , A d v a n c e s and P o t e n t i a l ( E d i t o r K a s h a , K . J . ). P r o c e e d i n g s of the F i r s t I n t e r n a t i o n a l S y m p o s i u m on Haploids, U n i v e r s i t y of Guelph, C a n a d a , 195209 (1974)

Acknowledgement We a r e g r a t e f u l to D r . R . J . B a k e r for a n i n t r o d u c t i o n to c o m p u t e r s i m u l a t i o n t e c h n i q u e s . R e c e i v e d J u l y 27, 1976 C o m m u n i c a t e d by R. R i l e y Literature B a r c l a y , I . R . : High f r e q u e n c i e s of h a p l o i d p r o d u c t i o n i n wheat (Tr/ticwm aestivum) by c h r o m o s o m e e l i m i n a t i o n . N a t u r e 256, 410-411 (1975) Bliss, F.A. ; Gates, C.E. : Directional selection in s i m u l a t e d p o p u l a t i o n s of s e l f - p o l l i n a t e d p l a n t s . A u s t . J . B i o l . Sci. 21, 705-719 (1968)

115

Dr. T . J . Riggs D r . J . W . Snape Plant Breeding Institute, M a r i s Lane, Trumpington, C a m b r i d g e CB2 2LQ ( E n g l a n d )

Effects of linkage and interaction in a comparison of theoretical populations derived by diploidized haploid and single seed descent methods.

Comparisons were made between the genetic means and variances of a quantitative trait determined by 8 loci in simulated populations of lines derived b...
457KB Sizes 1 Downloads 0 Views